Problem: Simplify the following expression: $k = \dfrac{20xy + 40y^2}{40zy + 10xy} - \dfrac{10xy + 60zy}{40zy + 10xy}$ You can assume $x,y,z \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{20xy + 40y^2 - (10xy + 60zy)}{40zy + 10xy}$ $k = \dfrac{10xy + 40y^2 - 60zy}{40zy + 10xy}$ The numerator and denominator have a common factor of $10y$, so we can simplify $k = \dfrac{x + 4y - 6z}{4z + x}$